Qualitative mathematical modeling for resilience assessment and management

Since the 1970s resilience has been a lively discussed concept in ecology and environmental management. Resilience refers to “a measure of the persistence of systems and of their ability to absorb change and disturbance and still maintain the same relationships between populations or state variables”. Despite important theoretical and empirical developments, the assessment of resilience of environmental systems has remained an unsolved challenge. Relevant variables and relations cannot always be immediately studied through exact equations or numerical methods. Variables usually differ in nature (e.g., natural, social), can be numerous, and might not be readily measured. The available data is commonly partial and not always quantitative. In this paper, assessing resilience of regimes of an environmental system will be based on the feasibility of representing regimes with loop models, which are developed with the qualitative mathematical modeling method of loop analysis. The importance of persistence in the definition of resilience calls attention to a mathematical treatment of stability in order to assess resilience. The present paper proposes that if a regime is resilient, the loop model representing the regime is stable. Correspondingly, if the regime is not resilient, the loop model representing the regime is not stable. In environmental management, promoting the persistence (resilience) of a desired regime, and the change of non desired ones, can be supported by analyzing what the influences (links) between the components of the regime are, or should be, so that the regime remains, or becomes, resilient and thus representable by a stable loop model. The approach introduced in the paper is explained with empirical evidences from three regimes observed in a wetland environment. It is shown that loop models can be obtained from scarce empirical data. Loop analysis allows alternative interpretations of the environmental system of interest, and addressing manifestations of non linearity.